SOLUTION: A person spins the pointer and is awarded the amount indicated by the pointer. (Here there is an image of a circle with a line straight down the middle seperating it in half and

Question 666521: A person spins the pointer and is awarded the amount indicated by the pointer.
(Here there is an image of a circle with a line straight down the middle seperating it in half and a line dividing the right side in half again. The left side (which is an entire half of the circle) is labled $2. The other half of the circle (which itself is divided in half horizontally) is labled $8 on the top and $12 on the bottom)

It costs $8 to play the game. Determine:

The expectation of a person who plays the game.

The fair price to play the game.

Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
To find the expected value of the game, you take all possible outcomes, multiply each by the probability of that outcome, and add them all up.

For this game, we have three possible outcomes: $2, $8, and $12. From your description of the game, the $2 space occupies half the spinner, and the $8 and $12 outcomes each occupy one fourth of the spinner. Assuming the pointer is completely fair, the probabilites are:
p($2) = 0.50
p($8) = 0.25
p($12) = 0.25

Multiplying each outcome by its probability, we get:
$2.00 * 0.50 = $1.00
$8.00 * 0.25 = $2.00
$12.00 * 0.25 = $3.00

Adding all these up gives us an expected outcome of $6.00 against the $8.00 cost to play the game.

Over time, a person playing the game should expect to lose an average of $2.00 per play.

You didn't define "fair" but I'm going to assume that it means that a player should expect to break even on average. With that definition, a fair price to play the game would be $6.00 per turn.
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